Grade 8 Decimal Operations: Unit Mastery Quiz with Full Solutions

Grade Level and Purpose

This record is a Grade 8 unit mastery quiz for Decimal Operations in the Number strand. It is intended for a learner who has already studied the unit and now needs a rigorous, self-contained assessment with full solutions.

This quiz samples the whole unit rather than reteaching it. For adjacent work with percents and decimal-percent conversions, see [rea.m08.number.ratios-rates-proportions.percent-bridges.unit-mastery-quiz]. For rate contexts that also require decimal computation, see [rea.m08.number.ratios-rates-proportions.unit-rates.unit-mastery-quiz].

What This Quiz Assesses

• Adding and subtracting decimals accurately
• Multiplying decimals with place-value reasoning
• Dividing decimals by whole numbers and decimals
• Estimating to check reasonableness
• Solving one-step and multi-step contextual problems
• Choosing correct units and interpreting results

Quiz Structure

• 10 questions
• 20 marks total
• Suggested time: 30 to 40 minutes
• Calculator: preferably not for Questions 1 to 8; optional for Questions 9 to 10 if the program permits

Mastery Recommendation

• Recommended mastery threshold: 16/20 (80%)
• In addition, the learner should earn at least 1 mark on each operation type:
  • addition/subtraction
  • multiplication
  • division
  • application/problem solving

Reason: a learner can sometimes compensate for a weak operation by succeeding on easier items elsewhere. The threshold above protects against that false mastery signal.

Marking Guidance

Award marks for:

• correct setup
• correct place-value treatment
• reasonable intermediate work
• correct final answer with units where needed

A small arithmetic slip with correct method can earn partial credit unless the question specifically targets computation fluency.

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Questions

1. Add.

Compute: 14.37 + 8.605

Marks: 2

2. Subtract.

Compute: 20 - 3.478

Marks: 2

3. Estimate, then calculate.

Estimate the sum, then find the exact answer: 6.89 + 12.14

Marks: 2

4. Multiply a decimal by a whole number.

Compute: 4.56 x 7

Marks: 2

5. Multiply two decimals.

Compute: 0.38 x 2.4

Marks: 2

6. Divide by a whole number.

Compute: 15.75 ÷ 3

Marks: 2

7. Divide by a decimal.

Compute: 8.64 ÷ 0.6

Marks: 2

8. Order of operations with decimals.

Compute: 3.5 + 2 x 1.24

Marks: 2

9. Money context.

A student buys 3 notebooks at $2.75 each and 2 pens at $1.40 each. They pay with $20. How much change should they receive?

Marks: 2

10. Measurement and multi-step reasoning.

A recipe uses 1.25 L of juice for one batch. A kitchen has 6.0 L of juice.

1. How many full batches can be made?
2. How many litres of juice will be left over?

Marks: 2

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Full Solutions and Marking Key

1. 14.37 + 8.605

Write the numbers so the decimal points line up:

14.370 +8.605 =22.975

Answer: 22.975

Marking:

• 1 mark for correct alignment/setup
• 1 mark for correct sum

2. 20 - 3.478

Rewrite 20 as 20.000.

20.000 - 3.478 = 16.522

Answer: 16.522

Marking:

• 1 mark for converting or aligning correctly as 20.000
• 1 mark for correct subtraction

3. Estimate, then calculate: 6.89 + 12.14

Estimate by rounding:

• 6.89 is about 7
• 12.14 is about 12
• estimated sum: 7 + 12 = 19

Exact calculation:

6.89 + 12.14 = 19.03

The exact answer is close to the estimate, so it is reasonable.

Answer: estimate 19; exact answer 19.03

Marking:

• 1 mark for a reasonable estimate
• 1 mark for correct exact sum

4. 4.56 x 7

Multiply as whole numbers first:

• 456 x 7 = 3192

Since 4.56 has 2 decimal places, place the decimal two places from the right:

• 31.92

Answer: 31.92

Marking:

• 1 mark for correct multiplication process
• 1 mark for correct decimal placement and final answer

5. 0.38 x 2.4

Multiply ignoring decimals first:

• 38 x 24 = 912

Now count decimal places:

• 0.38 has 2 decimal places
• 2.4 has 1 decimal place
• total: 3 decimal places

So the product is 0.912.

Answer: 0.912

Marking:

• 1 mark for correct product before placing decimal
• 1 mark for correct decimal placement

6. 15.75 ÷ 3

Divide:

• 15 ÷ 3 = 5
• 0.75 ÷ 3 = 0.25

So:

• 15.75 ÷ 3 = 5.25

Answer: 5.25

Marking:

• 1 mark for correct division setup/process
• 1 mark for correct quotient

7. 8.64 ÷ 0.6

To divide by a decimal, make the divisor a whole number. Multiply both numbers by 10:

8.64 ÷ 0.6 = 86.4 ÷ 6

Now divide:

• 86.4 ÷ 6 = 14.4

Check: 0.6 x 14.4 = 8.64, so the answer is correct.

Answer: 14.4

Marking:

• 1 mark for correctly scaling both dividend and divisor
• 1 mark for correct quotient

8. 3.5 + 2 x 1.24

Use order of operations: multiply before adding.

First:

• 2 x 1.24 = 2.48

Then:

• 3.5 + 2.48 = 5.98

Answer: 5.98

Marking:

• 1 mark for performing multiplication first
• 1 mark for correct final answer

9. Money context

Cost of notebooks:

• 3 x 2.75 = 8.25

Cost of pens:

• 2 x 1.40 = 2.80

Total spent:

• 8.25 + 2.80 = 11.05

Change from $20:

• 20.00 - 11.05 = 8.95

Answer: $8.95

Marking:

• 1 mark for correct total cost
• 1 mark for correct change with money units

10. Recipe context

Each batch uses 1.25 L. Total juice is 6.0 L.

Find number of batches:

• 6.0 ÷ 1.25 = 4.8

This means 4.8 batches in total are possible, but only 4 full batches can be made.

Juice used for 4 batches:

• 4 x 1.25 = 5.0 L

Leftover juice:

• 6.0 - 5.0 = 1.0 L

Answer:

1. 4 full batches
2. 1.0 L left over

Marking:

• 1 mark for identifying 4 full batches
• 1 mark for correct leftover amount with units

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Answer Key Only

1. 22.975
2. 16.522
3. estimate 19; exact 19.03
4. 31.92
5. 0.912
6. 5.25
7. 14.4
8. 5.98
9. $8.95
10. 4 full batches; 1.0 L left over

Common Errors to Watch For

• Misaligned decimals in addition or subtraction. Repair: line up decimal points, not the last digits.
• Incorrect decimal placement after multiplication. Repair: multiply first, then count total decimal places in the factors.
• Moving the decimal in only one number when dividing by a decimal. Repair: multiply both dividend and divisor by the same power of 10.
• Ignoring order of operations. Repair: do multiplication/division before addition/subtraction unless brackets change the order.
• Giving an impractical context answer. Repair: in real situations, check whether the answer must be a whole number of items or batches.

Interpretation of Results

• 18 to 20 marks: strong mastery; ready for mixed decimal, percent, and rate applications.
• 16 to 17 marks: secure mastery; continue with combined problem solving.
• 13 to 15 marks: partial mastery; review division by decimals and multi-step contexts.
• 12 or below: reteach core operations before moving on.

Record Positioning

This is an assessment record, not the main teaching record for the topic. It should be used after instruction and guided practice on decimal operations, and alongside linked quiz records for neighbouring percent and rate skills when building broader Grade 8 number fluency.